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middle diamond tensor product graph Diamond transformations Forcing Club Guessing PFA(S)[S] Closed coloring positive partition relation Absoluteness Universal Sequences strongly bounded groups Amenable C-sequence Shelah's Strong Hypothesis Mandelbrot set Whitehead Problem Antichain Iterated forcing Knaster and friends Selective Ultrafilter Uniformization Constructible Universe Generalized descriptive set theory OCA sap Reflecting stationary set Erdos-Hajnal graphs countably metacompact Forcing Axioms higher Baire space Sigma-Prikry O-space Singular cardinals combinatorics Fodor-type reflection Rock n' Roll projective Boolean algebra Diamond-sharp weak diamond Hindman's Theorem Filter reflection GMA ccc L-space Uniformly coherent Almost-disjoint family full tree Greatly Mahlo square principles incompactness very good scale Non-saturation Partition Relations nonmeager set stationary reflection specializable Souslin tree coloring number Large Cardinals indecomposable ultrafilter Kurepa Hypothesis free Boolean algebra stationary hitting Poset square Ostaszewski square Postprocessing function unbounded function Distributive tree Open Access Almost Souslin club_AD polarized partition relation Subtle tree property Martin's Axiom Singular Density Hereditarily Lindelöf space Erdos Cardinal Microscopic Approach Prevalent singular cardinals Well-behaved magma Sierpinski's onto mapping principle Ulam matrix Was Ulam right Coherent tree Subnormal ideal Axiom R Subtle cardinal Luzin set regressive Souslin tree Almost countably chromatic xbox Cardinal function Rado's conjecture Diamond for trees Minimal Walks Small forcing Chromatic number reflection principles Precaliber Successor of Regular Cardinal Reduced Power HOD Analytic sets PFA 54G20 ZFC construction Strongly Luzin set Fast club Jonsson cardinal Local Club Condensation. Parameterized proxy principle P-Ideal Dichotomy free Souslin tree Weakly compact cardinal Chang's conjecture Ineffable cardinal approachability ideal Cardinal Invariants Successor of Singular Cardinal Rainbow sets super-Souslin tree Generalized Clubs Aronszajn tree Ramsey theory over partitions Cohen real C-sequence Dushnik-Miller AIM forcing Slim tree S-Space weak square Nonspecial tree Vanishing levels Dowker space Commutative cancellative semigroups Strong coloring Knaster Ascent Path diamond star Prikry-type forcing Square-Brackets Partition Relations Hedetniemi's conjecture Singular cofinality Lipschitz reduction Fat stationary set Foundations Subadditive stick Souslin Tree Uniformly homogeneous b-scale Sakurai's Bell inequality SNR
Tag Archives: 03E50
Jensen’s diamond principle and its relatives
This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading